WASHINGTON — It was perhaps the one topic that received bipartisan attention Tuesday night — from President Barack Obama during his State of the Union address, in the official Republican response delivered by Sen. Marco Rubio of Florida, and in the tea party’s response to the response: the need to overhaul the nation’s immigration laws.

But despite the bipartisan call for broad action, partisan divides on how the complex topic should be tackled were on display Wednesday as the Senate held its first substantive hearing on the path forward.

Several Republicans on the key Judiciary Committee complained that the nation’s borders are not secure and that the latest efforts to change laws could lead to a new attempt at amnesty for illegal immigrants similar to those they have helped derail in the past.

Some Democrats stressed that a legal rewrite must recognize the rights of same-sex immigrant couples, an issue some Republicans involved in the effort have said could cost GOP support.

Still, members of Congress involved with bipartisan efforts to push immigration changes said Wednesday that they were encouraged by the urgency expressed by Obama during his State of the Union address, and that they will move ahead quickly while the nation’s attention is focused on the issue.

The four Democrats involved in a bipartisan group of eight senators who released a framework for revamping the system last month will huddle with Obama at the White House on Wednesday to update him, as they work to translate the brief document into a complicated bill.

Sen. Charles E. Schumer, D-N.Y., a member of the Judiciary Committee and the bipartisan group, told others on the panel Wednesday that they are “on track” to produce a bill by their targeted March time frame.

Schumer said Obama’s remarks on the issue Tuesday had been “just right.”

“He did not make it a wedge issue,” Schumer said. “He made it clear we have to act in a bipartisan way and gave us the space in our little group to come up with a bipartisan proposal.”

Later in the hearing, Sen. Lindsey O. Graham, R-S.C., another member of the group, asked Secretary of Homeland Security Janet Napolitano whether she had ever seen a better opportunity for a comprehensive bill.

“No,” she replied. “This is the moment.”

Napolitano told the committee that the U.S. border has never been more secure, describing efforts undertaken by Obama to enforce current law, including deporting more than 400,000 people since he took office.

“Our border is better staffed with more people, infrastructure and technology than at any time in our nation’s history,” she said.

That policy has not been popular with many immigrants, who say that despite an Obama promise to prioritize immigrants who have committed serious crimes, the deportations have swept up those with otherwise clean records and have separated families.

Napolitano was interrupted three separate times by activists protesting the deportation policy.

Republicans said those efforts have been insufficient.

Sen. Jeff Sessions, R-Ala., said he feared that despite discussions to pair better border security and new enforcement mechanisms with a path to citizenship, the efforts would instead amount to “amnesty only.”

“There’s a lot of overconfidence about this bill,” Sessions said, promising that if he thinks the legislation advanced by the bipartisan group does not include provisions to halt illegal immigration, “we’re going to expose it.”

“It will not pass,” he added.

Still, congressional negotiations on immigration have kicked into high gear in recent weeks. Sen. Patrick J. Leahy , D-Vt., who chairs the Judiciary Committee, which will be the gateway to Senate legislation, promised to quickly move legislation to the floor.

Republican leaders signaled a willingness to entertain the discussion by asking Rubio, another member of the Senate working group, to rebut Obama’s speech Tuesday.

In an interview with NBC’s “Today” show, House Speaker John A. Boehner, R-Ohio, praised the Senate group — and a parallel effort under way in the House — for the efforts.

“I would hope that the Senate players could continue to work in a bipartisan fashion. That’s the only way we’re gonna be able to address the big issues that face our country,” he said.

And Rep. Xavier Becerra, D-Calif., who has been negotiating with a bipartisan group of House members on the issue, told reporters that his group could roll out legislation “within the next few weeks.”

Included among those who testified at the Senate hearing Wednesday were Steve Case, former chief executive of AOL; Immigration and Customs Enforcement employee’s union representative Chris Crane; and Jose Antonio Vargas, a former Washington Post reporter who revealed in 2011 that he was brought to the country illegally by his parents as a child.